Dynamic calibration of force balances for impulse hypersonic facilities

This paper analyzes different techniques for the calibration of force balances for use in short-duration impulse hypersonic facilities such as shock tunnels. The background to how deconvolution can be used to infer aerodynamic forces on models in impulse hypersonic wind tunnels is presented along with the theory behind the different calibration techniques. Four calibration techniques are applied to a single-component stress-wave force balance. Experiments in the T4 shock tunnel using the balance demonstrate the suitability of the different calibrations for force measurements in an impulse facility. Cross checks between the calibration techniques are used to check their ranges of validity. It is shown that the impulse response derived from tests in which the model and force balance are suspended from a fine wire and the wire cut agree well with impulse responses derived from calibrations made using an impact hammer. The suitability of the balance for measuring dynamic forces is demonstrated by showing that the drag force on a model follows the history of Pitot pressure in the test section in the tunnel shots.Received: 17 May 2002, Accepted: 11 December 2002, Published online: 6 March 2003PACS: 47.40.Ki, 47.80.+v, 07.10.Pz     

Hypersonic flow over a multi-step afterbody

Effect of a multi-step base on the total drag of a missile shaped body was studied in a shock tunnel at a hypersonic Mach number of 5.75. Total drag over the body was measured using a single component accelerometer force balance. Experimental results indicated a reduction of 8% in total drag over the body with a multi-step base in comparison with the base-line (model with a flat base) configuration.The flow fields around the above bodies were simulated using a 2-D axisymmetric Navier–Stokes solver and the simulated results on total drag were compared with the measured results. The simulated flow field pictures give an insight into the involved flow physics. Communicated by K. Takayama PACS 47.40.Ki     

Drag measurements at Mach 5 using a stress wave force balance

The stress wave force balance, which has been used for measurements of drag on short models in hypersonic impulse facilities, is investigated here for its suitability for drag measurements on a longer, axisymmetric model. The sensitivity of the balance to loading distribution is investigated and results are reported for experiments on a 5° semi-angle cone, 425 mm in length and of 1.71 kg mass. Experimental drag measurements are shown to be in good agreement with theoretical levels. An investigation into the period over which the stress wave force balance can be used is addressed and, for the present model, the balance is shown to be suitable for measurements in flows of durations of one to several milliseconds with an estimated accuracy of ±10%.     

Drag force on quasi-axisymmetric scramjets at various flight Mach numbers: theory and experiment

The net axial force on a non-fuelled quasi-axisymmetric scramjet model designed for operation at Mach 6 was measured in the T4 Stalker tube at The University of Queensland using a single-component stress wave force balance. The design used was a variant of a model that was tested previously at Mach 6. The new model was equipped with a modified thrust nozzle that was designed to improve the performance of the nozzle. Tests were performed to measure the drag force on the model for Mach 6, Mach 8 and Mach 10 shock tunnel nozzles for a range of flow conditions. The nozzle-supply enthalpy was varied from 3 to 10 MJ/kg and the nozzle-supply pressure from 35 to 45 MPa. For the test model, the drag coefficient increased with increasing nozzle-supply enthalpy. The test results are compared with a force prediction method based on simple hypersonic theories and three-dimensional CFD. The test results are in good agreement with the predictions over the wide range of conditions tested. The re-designed model has a more efficient nozzle but this comes at the expense of increased drag associated with the modifications required for the cowl. The results indicate that this type of vehicle design is not likely to be suitable for flight above Mach 8.

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Shock tunnel study of spiked aerodynamic bodies flying at hypersonic Mach numbers

A three-component accelerometer balance system is used to study the drag reduction effect of an aerodisc on large angle blunt cones flying at hypersonic Mach numbers. Measurements in a hypersonic shock tunnel at a freestream Mach number of 5.75 indicate more than 50% reduction in the drag coefficient for a 120° apex angle blunt cone with a forward facing aerospike having a flat faced aerodisc at moderate angles of attack. Enhancement of drag has been observed for higher angles of attack due to the impingement of the flow separation shock on the windward side of the cone. The flowfields around the large angle blunt cone with aerospike assembly flying at hypersonic Mach numbers are also simulated numerically using a commercial CFD code. The pressure and density levels on the model surface, which is under the aerodynamic shadow of the flat disc tipped spike, are found very low and a drag reduction of 64.34% has been deduced numerically.     

Design of a pulse-type strain gauge balance for a long-test-duration hypersonic shock tunnel

When the measurement of aerodynamic forces is conducted in a hypersonic shock tunnel, the inertial forces lead to low-frequency vibrations of the model, and its motion cannot be addressed through digital filtering because a sufficient number of cycles cannot be obtained during a tunnel run. This finding implies restrictions on the model size and mass as the natural frequencies are inversely proportional to the length scale of the model. Therefore, the force measurement still has many problems, particularly for large and heavy models. Different structures of a strain gauge balance (SGB) are proposed and designed, and the measurement element is further optimized to overcome the difficulties encountered during the measurement of aerodynamic forces in a shock tunnel. The motivation for this study is to assess the structural performance of the SGB used in a long-test-duration JF12 hypersonic shock tunnel, which has more than 100 ms of test time. Force tests were conducted for a large-scale cone with a \(10^{\circ }\) semivertex angle and a length of 0.75 m in the JF12 long-test-duration shock tunnel. The finite element method was used for the analysis of the vibrational characteristics of the Model-Balance-Sting System (MBSS) to ensure a sufficient number of cycles, particularly for the axial force signal during a shock tunnel run. The higher-stiffness SGB used in the test shows good performance, wherein the frequency of the MBSS increases because of the stiff construction of the balance. The experimental results are compared with the data obtained in another wind tunnel and exhibit good agreement at \(M = 7\) and \(\alpha =5^\circ \).     

Supersonic drag of three-dimensional bodies with a star-shaped cross section and its calculation

The effect on the aerodynamic drag of the real properties of the gas in the shock layer around pyramidal star-shaped bodies (the viscosity, the displacement thickness of the boundary layer, its separation under the influence of the inner shocks) is considered. It is shown that the models for calculating the total drag of star-shaped bodies which do not take into account the displacement thickness of the boundary layer are applicable only at low supersonic free-stream velocities (M < 3). A model of the boundary layer displacement thickness is proposed and tested over a broad range of variation of the parameters that determine the geometry of the pyramidal bodies for high supersonic or hypersonic speeds. A comparison with the experimental data shows that the calculation procedure adequately reflects the results of experiments on the aerodynamic drag of star-shaped bodies in cases in which the inner shocks in the shock layer do not lead to boundary layer separation and can be used in optimization problems.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.1, pp. 57–69, January–February, 1993.     

On the front condition for compositional gravity currents

A two-dimensional potential flow is employed to derive the front condition of the gravity current. The derivation starts from the balance between the static pressure of the gravity current and the form drag imposed on the gravity current by the ambient fluid. After employing Bernoullis equation along the interface of the gravity current near the head, we end up with a front condition that is in better agreement with experiment than previous theoretical models. This condition is a function of the density ratio between current and ambient fluids, which was different from previous theoretical models, while it has been widely used in experimental studies. The present front condition suggests that the form drag may account for a significant part of the resistance force applied on the current head.     

Dfag measurements on star-shaped body at m ≈ 6 and 8

Results have been obtained in recent years which make it possible to get an idea of the optimal shape of a three-dimensional body at high supersonic speeds. It has been shown [1–6] that bodies with a cross section in the form of a star with certain limitations have the least wave drag and remain optimal with respect to total drag with approximate account for the friction forces. The transition from the optimal body of revolution to the star-shaped body of equivalent volume and length makes a several-fold drag reduction. These theoretical results, initially obtained on the basis of the Newton drag law, were then confirmed by the exact solution [7] for bodies which were close in form to the optimal. Subsequent experimental studies investigated the flow pattern between two lobes representing an element of the star over a wide range of included angles. The experiments showed that there actually exists a flow between the rays corresponding to the solution [7], that this flow is stable, and that the wave drag calculated from the pressure distribution over the body surface is several fold less than for the equivalent cone. Although these results are encouraging, they do not prove the advantages of the star-shaped form for practical use. The point is that the star has considerably more wetted area; therefore the effect of the marked reduction of the wave drag may be compensated by an increase of the friction drag. The references above to the theory which considers friction are not convincing, since the friction estimates are approximate, while real friction is complicated by the presence of shock waves within the flow, the possibility of a turbulent boundary layer, separation, etc. Not all these factors are amenable to calculation, and it is clear that conclusions can be drawn on star drag only after making direct measurements of the total force acting on a model in a flow.In the following we describe the results of force tests conducted with a star model at M6 and 8. During the tests the flow pattern in the wake behind the body was photographed in addition to the force measurements.The authors wish to thank G. I. Petrov, G. G. Chernyi, M. Ya. Yudelovich, and A. A. Churilin for assistance in carrying out the experimentation.     

Similitude of hypersonic flows of low-density gas over blunt bodies

Laws of similitude of hypersonic flows of monatomic gases have been obtained earlier from asymptotic analysis of the equations as S and confirmed by experimental data and numerical results [1], For diatomic gases, dimensionless numbers have not been deduced by analyzing the equations but by general arguments based on analogy with monatomic gases; they were used to compare experimental and calculated results in [1–3]. In the present paper, dimensionless numbers are derived on the basis of model kinetic equations for a diatomic gas, and limits of their applicability are established. Numerical calculations confirm the exact and approximate laws of similitude and permit a comparison with experimental results. The influence of the laws of viscosity on the drag for a sphere as a function of the Reynolds number Re₀ determined using the viscosity at the stagnation point is investigated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 130–135, March–April, 1981.     

Optimal blunt-nosed figures of revolution in a gas of different rarefactions

Many studies have been made of the optimization of the shape of bodies in a gas stream. However, the majority of these have been made for supersonic and hypersonic flow in the limiting case of a continuum [1], and only a few studies have been made [1–3] for the case of flow over a body of a rarefied gas (mainly a free molecular stream). In the present paper, the problem of shape optimization is considered for hypersonic flow of a gas of different rarefactions over a body. Numerical methods are used to investigate the influence of the Reynolds number on the shape and drag of optimal figures of revolution.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 158–161, May–June, 1980.     

Direct drag measurements in a turbulent flat-plate boundary layer with turbulence manipulators

The effect of turbulence manipulators on the turbulent boundary layer above a flat plate has been investigated. These turbulence manipulators are often referred to as Large Eddy Break Up (LEBU) devices. The basic idea is that thin blades or airfoils are inserted into the turbulent flow in order to reduce the fluctuating vertical velocity component v above the flat plate. In this way, the turbulent momentum transfer and with it the wall shear stress downstream of the manipulator should be decreased. In our experiments, for comparison, a merely drag-producing wire also was inserted into the boundary layer.In particular, the trade-off between the drag of the turbulence manipulator and the drag reduction due to the shear-stress reduction on the flat plate downstream of the manipulator has been considered. The measurements were carried out with very accurate force balances for both the manipulator drag and the shear stress on the flat plate. As it turns out, no net drag reduction is found for a fairly large set of configurations. A single thin blade as a manipulator performed best, i.e., it was closest to break-even. However, a further improvement is unlikely, because the device drag of the thin blade elements used here has already been reduced to only that due to laminar skin friction, and is thus the minimum possible drag. Airfoils performed slightly worse, because their device drag was higher. A purely drag-producing wire device performed disastrously. The wire device, which consisted of a wire with another thin wire wound around it to suppress coherent vortex shedding and vibration, was designed to have (and did have) the same drag as the airfoil manipulator with which it was compared. The comparison showed that airfoil and blade manipulators recovered 75–90% of their device drag through a shear-stress reduction downstream, whereas the wire device recovered only about 25–30% of its device drag.Conventional LEBU manipulators with airfoils or thin blades produce between 0.25% and 1% net drag increase, whereas the wire device (with equal device drag) produces as much as 4% net drag increase. These data are valid for the specific plate length of our experiments, which was long enough in downstream extent to realize the full effect of the LEBU manipulators. Turbulence manipulators do indeed decrease the turbulent momentum exchange in the boundary layer by rectifying the turbulent fluctuations. This generates a significant shear-stress reduction downstream, which is much more than just the effect of the wake of the manipulator. However, the device drag of the manipulator cannot be reduced without simultaneously reducing the skin friction reduction. Thus, the manipulator's device drag exceeds, or at best cancels, the drag reduction achieved by the shear-stress reduction downstream. A critical survey of previous investigations shows that the suggestion that turbulence manipulators may produce net drag reduction is also not supported by the available previous drag force measurements. The issue had been stirred up by less conclusive measurements based on local velocity data, i.e., data collected using the so-called momentum balance technique.List of symbols b lateral breadth of test plate - c chord length of turbulence manipulator - d diameter of wire manipulator - e distance of the elastic center from the leading edge of the manipulator airfoil - h height of manipulator above test plate - q dynamic pressure of the potential flow above the test plate - s spacing of turbulence manipulator elements - t thickness of turbulence manipulator elements - u,v,w fluctuating velocities in downstream, platenormal, and lateral directions - x distance from the leading edge of the test plate in the downstream direction - x ₀ location of the trailing edge of the first manipulator - z distance from test plate center in the lateral direction - C _D drag coefficient - C _L lift coefficient - D _m drag of manipulated plate including device drag and shear stress, calculated from manipulator location to downstream location - D ₀ drag of unmanipulated plate boundary layer, consisting of the shear stress calculated from manipulator location to downstream location - F drag force - F ₀ total skin friction force, measured over a distance from 0.4 m upstream of manipulator to 6.35 m downstream of manipulator, measured without turbulence manipulator - F _LEBU device drag force of the LEBU, i.e., the turbulence manipulator - F _m total drag force of manipulated plate, consisting of - F _LEBU and skin friction force, measured over a distance from 0.4 m upstream of manipulator to 6.35 m downstream - F _cf skin friction force as measured by the floating element balance, manipulated case - F _cfo skin friction force, as measured by the floating element balance, unmanipulated case - F _cf skin friction saving, defined as F _cf = F _cf – F _cfo - F _cf cumulative skin friction savings, i.e., the sum of the skin friction savings F _cf , added up from the location of the manipulator to the downstream location , as shown in Fig. 11. In Fig. 13 the cumulative skin friction savings are summarized up to their asymptotic value, reached at 200 - Re _c Reynolds number of the manipulator elements, calculated with the chord length c and the local velocity in the boundary layer - Re ₀ Reynolds number at the location x ₀ of the manipulator, calculated with the momentum thickness of the boundary layer and the mean flow velocity U - U mean flow velocity in the potential regime of the wind tunnel test section - angle of attack of the manipulator airfoils - ₀ boundary layer thickness at the location x ₀ of the manipulator - dimensionless distance from the manipulator in the downstream direction, defined as - density of the air - ₀ local skin friction shear stress, unmanipulated case - _{0 Average} skin friction shear stress, average value over the lateral span (b = 2 m) of the test plate, unmanipulated case - _m local skin friction shear stress, manipulated case - momentum thickness of the undisturbed turbulent boundary layer at the location x ₀ The authors would like to thank Prof. H. H. Fernholz for his scientific and administrative support. The hardware for the experiments was designed and built by C. Daase, W. Hage and R. Makris. Funding for the project was provided by the Deutsche Forschungsgemeinschaft and is gratefully acknowledged.     

Magnetohydrodynamic control of supersonic flow past bodies: Possibilities and undesirable effects

Basic problems of super-and hypersonic magnetohydrodynamics (MHD) associated with the determination of the integral characteristics of bodies and vehicles inside which there are systems generating a uniform magnetic field are considered. Three classes of flows, namely, flow in a hypersonic multimode fixed-geometry air-intake; internal and external flow in a model of a hypersonic vehicle containing an air-intake with an MHD generator, a combustion chamber, and a supersonic nozzle; and hypersonic flow past a blunt cone are studied using numerical simulation and theoretical analysis (on the basis of the complete averaged system of Navier-Stokes equations and the electrodynamic equations). Attention is concentrated on the presence of an additionalmagnetic force acting on the system generating themagnetic field and, consequently, on the body and initiating an additional drag (in the case of a vehicle-reducing its thrust). Attractive possibilities for MHD flow control, namely, an increase in the degree of flow compression in the air-intake, a reduction in the ignition length in the combustion chamber, and a decrease in the heat flux to the nose of the body, are noted, as well as negative effects associated with the action of the magnetic force on the bodies considered.     

Re-entry body drag: shock tunnel experiments and computational fluid dynamics calculations compared

The best approach for conducting the research necessary for developing hypersonic flight vehicles is a close coupling between experiments that employ rapid measurement techniques and computational fluid dynamics (CFD) that appropriately accounts for the freestream nonuniformities, as well as for hypervelocity flow phenomena. This approach has been employed here, where stress wave force measurements and CFD calculations have been combined in an investigation of the axial drag on a generic re-entry body. Experiments were performed in argon and nitrogen, with test flows ranging in total enthalpy between 3 MJ/kg and 12 MJ/kg and Mach numbers varying from 6 to 13. The associated measured drag forces ranged from 300 to 360 N. For Mach 12 argon flows, the CFD overpredicted the drag by 8%, while for two hypervelocity nitrogen flows the CFD overpredicted the drag by at most 5%. Considering uncertainties in the force measurements and the CFD boundary conditions, the agreement is good, and the work highlights both the ability of the force measurement technique to respond to rapid changes in flow conditions and the importance of carefully accounting for flow gradients in the CFD boundary conditions. This paper was based on work that was presented at the 3rd International Symposium on Interdisciplinary Shock Wave Research, Canberra, Australia, March 1–3, 2006.     

Numerical simulations of drop size evolution in a horizontal pipeline

A population balance model using a standard method of moments ($S-\gamma$) in an Eulerian–Eulerian framework has been used for oil and brine two-phase flow simulations in pipelines. Results have been compared to both numerical and experimental data from the literature. The effects of the forces constituting the momentum transfer term at the interphase between droplets and the continuous phase (drag, lift, turbulent dispersion and virtual mass), turbulence modelling, break-up and coalescence parameters are analysed; they are shown to be important for droplet mean diameter evolution. It has been demonstrated that a correct combination of models and parameters improves (47% for the best case) simulated results when compared to experimental data. Interactions between the different components of the whole model are discussed and their corresponding effects on the droplet diameter predictions are explained. In particular, the addition of the lift force tends to push the droplet toward the walls of the computational domain where turbulence and shear stress are the strongest, therefore leading to an increased break-up rate. Based on the findings of this study, recommendations for further population balance-based modelling with a standard method of moments are provided.     

Size prediction of κ-carrageenan droplets formed in co-flowing immiscible liquid

The formation of κ-carrageenan droplets in channel emulsification was experimentally investigated. The dispersed phase was vertically injected into co-flowing immiscible palm oil in the direction of gravity. This study focused on predicting κ-carrageenan drop size using force balance analysis. The force balance model considers the interfacial tension to be the solitary attaching force, while a combination of the drag force from the co-flowing palm oil and the body force of the extruding κ-carrageenan liquid act as the detaching forces. The conventional model gave poor predictions for droplet size, with an average relative deviation of 23%. This large deviation could be attributed to necking phenomena and an underestimation of the drag force generated on the shear-thinning κ-carrageenan solution. By incorporating correction factors, the average relative deviation of the force balance model dropped to 4%.     

Aerodynamic force measurement using 3-component accelerometer force balance system in a hypersonic shock tunnel

A new three-component accelerometer force balance has been designed, calibrated and tested in hypersonic shock tunnel (HST2) of Indian Institute of Science. The newly designed balance is able to measure aerodynamic forces (within test time of one millisecond) on test models at angles of attack from 0 to 12°. Two models, a blunt cone with after body and a blunt cone with after body and frustum are used to establish the accuracy of the force balance. The tests were conducted for the above two configurations with a constant Mach number of 8 and total enthalpy of 2.0 MJ/kg. The effectiveness of the balance is demonstrated by comparing the forces and moments of measured data with AGARD models. The flow fields around the test model are simulated using a 3D axisymmetric Navier–Stokes solver and the simulated results were compared with the measured values. Measured and computed force data are matched within ±10% for two different models tested here. The accuracy of the force balance is also estimated with the Newtonian theory and the values are approximately ±10% for the axial component and ±8% for the normal and pitching moment components.      

On the Viscous Drag of a Plate with Spherical Recesses

The drag of flat plates with spherical recesses was measured using the direct balance method. The experiments were run in a low-turbulence wind tunnel with a cross-section measuring 1000 × 1000 mm and a length of 400 mm. Three surfaces with recesses 7.0, 3.9, and 1.3 mm in diameter and 0.5, 0.3, and 0.2 mm deep, respectively, were tested. It is shown that on the Reynolds and Mach number ranges Re= (3–9)· 10⁶ and M 0.3 the spherical recesses add to the drag of a flat plate in turbulent flow. The recesses have almost no effect on the location of laminar-turbulent transition, which occurs at Re_t 3· 10⁶.     

Effects of the history force on an oscillating rigid sphere at low Reynolds number

The present work presents an experimental study on a free-falling rigid sphere in a quiescent incompressible newtonian fluid, placed in an oscillating frame. The goal of this investigation is to examine the effect of the history force acting on the sphere at small Reynolds numbers (Re2.5) and finite Strouhal numbers (1Sl20). The particle trajectory is measured by using a high-speed video camera and modern techniques of image processing. The average terminal velocity, the oscillation magnitude, and the phase shift with the oscillating frame are measured and compared with those obtained from theoretical approaches. The comparison is made by solving the equation of motion of the sphere with and without the history force. In addition to the significant role that this force plays in the momentum balance, it was found that the correction of the added mass force and the history force by the empirical coefficients of Odar and Hamilton (J Fluid Mech 18:302–314, 1964; J Fluid Mech 25:591–592, 1966) are not necessary in our Re and Sl ranges. The added mass is the same as that obtained by the potential flow theory and the history force is well predicted by the Basset expression (Treatise on hydrodynamics, 1888).     

乘波体前体/进气道一体化设计研究

为了研究乘波体几何外形参数和飞行参数对前体/进气道一体化设计的影响,采用理论分析和数值模拟相结合的方法,以马赫数Ma=6和攻角α=0为设计状态、进气道总压恢复系数和前体阻力系数为目标函数,对乘波体前体/进气道进行了优化设计,并在此基础上研究了攻角、马赫数、前缘半径、前体宽度对气动参数的影响。结果表明:该乘波体前体/进气道构型具有良好的攻角特性,总压恢复系数比基准构型提高17.79%,阻力系数比基准构型降低78.5%,符合高超声速飞行器高升力、低阻力的要求,且非常适合小攻角高超声速巡航飞行;为了得到较高升阻比的前体,在前缘半径R≤2mm的范围内进行流场反设计时,可以将设计马赫数的取值比预期低一些。